I would only apologize to his daughter if you felt you were in the wrong. That wasn't the confrontation I had in mind. It would go more like "I feel like you don't respect me. I'm married to your father, I'd like to stay married to your father, but I also have limits in terms of how I will be treated. I'm not asking you to like me, but I would like to find a way for us to have a relationship based on mutual respect. We have had some tough times in the past that both of us contributed to, I'm willing to let that go. What do you need from me to feel that we can have a productive relationship?" etc. etc. etc. Listen to what she has to say, validate what you agree with. If you don't agree, tell her so, but do it from the perspective of looking for compromise versus arguing. It's ok to agree to disagree. You're looking to be conciliatory, but you're not looking to be submissive, now or in the future.
It might be that after she has that conversation with you a weight will lift from her shoulders as well because she'll know you're not holding a grudge and the air has been cleared.
I would not do that with H present, I would do it one-on-one, and then tell H you did it, but don't go into the details.
Even though she no longer lives with you, you will still need to set and enforce boundaries, and clearly going to H is not effective enforcement. You need to think about how you can enforce your boundaries yourself via what you will and will not do. "I will not be spoken to like that, if you speak to me in that manner, I will simply walk away". "I will not clean up after you. If you leave dirty dishes, they will stay dirty until you or your father wash them". Those consequences are about what YOU will do.
Labug may be able to help you more as I know she's done quite a bit of work on boundary setting.
I definitely think the key to your sitch lies in reaching an accord with the daughter without H involved at all. You'd almost benefit from going to an MC with her versus H.
That's not to say that you're going to come out with a Hallmark holiday card relationship with her, just a relationship that you both understand and agree to. You could then present that to H as "the way things are going to be" and he can accept or reject it. If he's willing to work with you, then you'll need to set boundaries there too -- H shouldn't take sides. He should just excuse himself and tell the two of you to work it out. That way he doesn't have to make choices. If either one of you comes to him to complain about the other, he should tell you to "talk to the hand". That way, he can have whatever relationship he wants with both of you without getting caught in the middle.
This is going to come down to boundary setting and enforcement assuming you can hammer out an understanding with SD, that would be your simultaneous challenge.
Accuray
Married 18, Together 20, Now Divorced M: 48, W: 50, D: 18, S: 16, D: 12 Bomb Dropped (EA, D): 7/13/11 Start Reconcile: 8/15/11 Bomb Dropped (EA, D): 5/1/2014 (Divorced) In a New Relationship: 3/2015